create the following procedure, then to call it: type "call sort_categories;" in mysql.

gistfile1.txt

delimiter ;;
    drop procedure if exists sort_categories;;
    create procedure sort_categories()
    begin
        DECLARE cur_id BIGINT UNSIGNED;
        DECLARE cur_eof INT DEFAULT FALSE;
        DECLARE cur CURSOR FOR 
            SELECT entity_id 
            FROM catalog_category_entity_varchar 
            WHERE attribute_id = (
                SELECT attribute_id 
                FROM eav_attribute 
                WHERE attribute_code = 'name' 
                AND entity_type_id = (
                    SELECT entity_type_id 
                    FROM eav_entity_type 
                    WHERE entity_type_code = 'catalog_category'
                )
            ) 
            ORDER BY value ASC
        ;
        DECLARE CONTINUE HANDLER FOR NOT FOUND SET cur_eof = TRUE;
        SET @i:=0;
        OPEN cur;
        runForEach: LOOP
            FETCH cur INTO cur_id;
            IF cur_eof THEN
                LEAVE runForEach;
            END IF;
            SET @i:=@i+1;
            UPDATE catalog_category_entity SET position = @i WHERE entity_id = cur_id;
            SELECT @i;
        END LOOP runForEach;
        CLOSE cur;

    end 
;;